This section provides a comprehensive review of the literature in the area of Efficiency measurement and Data Envelopment Analysis. Measuring Commercials banks efficiency has emerged across the globe, which the literature review aspect has been explored in great amount by economists and numerous scholars. Many theoretical an empirical study showed that Commercial banks in UK plays an important role in the financial market of the UK economic and hence it is important to measure whether this commercial banks operate efficient on not. The preferred method used in this is study is Data Envelopment Analysis (DEA); which have been used by various writers to examine the efficiency of banks across the world and there are a number of papers that have used non-parametric methods for measuring the efficient banks; for example, Berg et al (1991); Berger et al (1993); Ferrier and Lovell (1990) and Fucuyama, H., 1993. Technical and scale efficiency of Japanese commercial banks: a non parametric approach. Appl. Econ. 25, pp. 1101–1112.Fucuyama (1993) and in Berger and Humphrey (1997) they surveyed 130 studies that applies frontier efficiency method to financial institutions in 21 countries, although their research is limited to efficient frontier techniques (e.g. DEA, stochastic frontier analysis). Furthermore, ever since that time, numerous papers have been published and in Seiford (1994) study of DEA there was 472 published articled on DEA Bibliography listed. In this study using DEA to measure UK commercial banks, can be differentiated on the basis of the data sample of this banks and the number of banks used, methodology, and considered variables and the analysed result.

This study used the methods that are developed by Allen N. Berger and David B. Humphrey (1992). In their paper “Measurement and Efficiency Issues in Commercial Banking”, they carried out three alternative methods which are, The Asset, The User Cost, and the Value-added method in choosing bank outputs. Under the asset methods according to Sealey and Lindley (1977), Loans and other assets are considered to be bank outputs; while deposits and other liabilities are inputs. The User Cost methods is basis of its net contribution to bank revenue and Hancock (1985a, 1985b) and Fixler and Zieschang (1990) used the user cost method to determine the weights applied to bank asset and liability. While the Value-added method

In this literature review, we address these issues in four main ways, first, we extensively review several research studies on the causes and consequences of efficiency measurement, secondly, we will introducing the non-parametric Data Envelopment Analysis and deal with the motivation behind choosing Data Envelopment and the result of our findings and contributions, thirdly we will given a brief comparisons of nonparametric data envelopment analysis (DEA) and the parametric stochastic frontier analysis (SFA) the two main method of measuring efficiency and come to the conclusion why the method that is used in the study is preferable and fourthly, analyze cross-border banking efficiency on data envelopment analysis (DEA) in a single county ad also in more than one country, drawing to the final review of by looking at various view from analysts and economist that has contributed to the data envelopment analysis (DEA) mainly for banks purpose

Firstly, we will look at the overview of efficiency measurement by looking at previous studies on several different perspectives in measuring efficiency in Banks

In the USA, Sherman and Gold (1985) used the DEA method to measure the efficiency of savings bank with 14 branch offices. In their findings, DEA results showed that six banks branches were operating inefficiently and these branches should explicitly consider the mix of services provided and the resources used to provide services by the other efficient operating bank branches. Relative study was carried out by Parkan (1987), he found that eleven banks branches out of thirty-five banks braches were relatively inefficient.

Using DEA methods to measured the efficiency in U.S. banking on the sample of 322 independent banks, Ferrier and Lovell (1990) in their study, found that the average bank used 21 percent more inputs than necessary, approximately three-quarters of which was technical inefficiency

Alsi Aly, Grabowski, Pasurka, and Rangan (1990) they used DEA in their study; and found that banks could have employed 35 percent fewer inputs without reducing output.

As well, Elyasiani and Mehdian (1990) used the DEA method; also found that banks over employed inputs by about 12 percent.

In the Barr et al. (1992, 1993, 1994, 1997, 1998, and 1999) Using the DEA model, a bank is a transformer of multiple inputs into multiple outputs and a bank’s DEA efficiency score from this captures the essential financial intermediation functions of a bank.

Fernandez-Castro and Smith (1994) study using the nonparametric DEA method for ratio analysis. In their result it was showed that corporate efficiency is multidimensional in nature and that there exist a variety of indicators of corporate efficiency.

Berg, Forsund and Jansen (1992) & Zaim (1995) studies of measurement of the efficiency change in the banking industry during the deregulation period 1980-1989. In their studies using the Norwegian and Turkish banks sample, they suggested that financial improvement can improve efficiency and that banks can experience improved efficiency after deregulation.

Measuring the technical efficiency of 201 large sized US Banks, Miller and Noulas (1996), result show an overall technical efficiency of around 97 percent; nonetheless, majority of these banks were too large and experiencing decreasing returns to scale. And their second-stage regression study showed that pure technical efficiency is positively related to these large bank sizes and their profitability.

Using DEA Method, Peristiani (1996) and DeYoung (1997) both found that measuring cost efficiency can be positively related to examiners’ ratings of bank management quality. Moreover, later study found that banks’ management ratings were more strongly related to their asset quality ratings than to any of their other examination ratings.

Measuring the efficiency of Nigeria banks, Ayadi et al (1998) using the DEA method to study ten banks by using the financial data from 1991 to 1994. Using the input and output variable selection; (input: interested paid on deposit, total expenses and total deposit) while (output: total loan interest and non-interest income), in their find they showed that banks in long period of existence are relatively efficiency than new bank.

Using DEA with three inputs and two outputs, Chu and Lim (1998) measured the cost and profit efficiency of a panel of six Singapore banks during the period 1992- 1996. In their result, it was showed that during this period the six banks have higher overall efficiency of 95.3% compared to profit efficiency of 82.6%. In addition, they also showed that the large Singapore banks have higher efficiency of 99.0% compared to the 92.0% for the small banks.

Alirezaee et al. (1998) using DEA method to study the efficiency of 1,282 bank branches in Canada, in their results from the total number of inputs and outputs; they found that the average branch efficiency score varies inversely with the number of branches . The cause of this bias in efficiency scores; as they advice was as a result of using relatively small sample sizes (three inputs and three outputs).

Using DEA method during the period of 1997, Leon (1999) measured the cost frontier estimation of 23 Mexico banks. And from her result it showed that the system average was 39% inefficiency; and mostly the large banks and the foreign banks that indicate to be the inefficiency ones.

Alam (2001), study of nonparametric DEA method to measure the efficiency of large U.S. banks from the period of 1980-1989 and in his findings he reported that a statistically significant efficiency for these large U.S. banks. This was mainly caused by the technological change rather than the changes in overall technical and scale efficiencies.

By using DEA method Cook and Hababou (2001) studied both the sales and service efficiencies of bank branches and using the linear programming DEA modelling method they were able to derive the best efficiency scores by accounting for the bank branch resource inputs.

In the UK, Drake and Howcroft (2002) measured the relative efficiency of the clearing bank branches using DEA method. Their study used the basic efficiency indices and extended the analysis by examining the relationship between size and efficiency

Akhtar (2002) used the DEA method on 40 sample commercial banks of Pakistan to measure the efficiency. In his study, it was found that under the constant returns to scale (CRS) DEA, the overall efficiency score for Pakistani commercial banks for the year 1998 was 80%. In comparison to this study the Pakistan efficiency score are lesser than the world mean efficiency.

In addition, Kumbhakar and Sarkar (2003) study the relationship between deregulation and efficiency improvement using data from the Indian banking industry over a 12-year period from 1985 to 1996. In their finding it showed that private banks efficiency improves in response to the deregulation measure and these does not affect public

In contrast, studies from Bauer et al (1993); Elyasiani and Mehdian (1995) and Halkos and Salamouris (2004) that used DEA to measured the efficiency of the Greek banking sector during 1997-1999, which is when various financial reforms took place, and they find that financial reform has no capability lead to efficiency effectiveness.

Using the sample period of 1992 – 2002, Zuniga (2005), developed a non-parametric cost function method to solve the section and simultaneity problem. In his result it was showed that the average efficiency was approximate highly by 15% in comparison to the beginning of the period.

Recently, Lo and Lu (2006) used a two-stage DEA method that included profitability and marketability to study the efficiency of financial holding companies (FHCs) in Taiwan. Their aim was to identify the most important inputs/outputs and to distinguish those FHCs which are treated as benchmarks. In their Results it is showed that big-sized FHCs are generally more efficient than small-sized ones.

Das and Ghosh (2006) used DEA to measure the efficiency of Indian commercial banks during the period of 1992-2002. They found that medium-sized public banks performed reasonably well and efficiency improved.

In Wu et al. (2006) study of DEA and neural networks (NNs) methods in measuring the relative bank branch efficiency of a large Canadian bank. In their results it was proposed that the measuring of efficiency using the DEA-NN method has good correlation with that of measurement using the DEA method, also they showed that their measurement of efficiency using the DEA-NN method was also a good alternative to the traditional DEA method that every economist are familiar with.

Chuling (2009) studied the efficiency of banks in Sub Saharan African using DEA. In his work, these banks could save 20 – 30% of their total cost if they were operating efficiently (operating on the frontier), and in addition to his finding the foreign-owned banks are more efficient than the public banks and domestic private banks.

General used of DEA measuring of efficiency and the motivation behind choosing Data Envelopment and the result of our findings and contributions

DEA studies have been used to measured efficiency in different field/ industry besides the commercial banking industries which these study focus on and there is a wealth of literature on both basic and applied research in DEA. For example, in Dimitras et al. (1996) study, various DEA techniques were used in the prediction of business failures but their focus was on industrial firms. Using DEA Smith and Gupta (2000) provide a discussion of the application of neural networks in business problems.

Board et al. (2003) survey O.R. applications in the financial markets. Zhou and Poh (2008) provide a recent survey of DEA applications but they focus on energy and environmental studies. More recently, Cook and Seiford (2009) review the methodological developments of DEA over the last thirty years. However, they do not discuss applications of DEA. The above reviews are quite general and they do not focus on applications in banking.

Thirdly brief comparisons of nonparametric data envelopment analysis (DEA) and the parametric stochastic frontier analysis (SFA) and come to the conclusion why the method that is used in the study is preferable

Literature review on efficiency study is controlled by the two most popular methods: the nonparametric data envelopment analysis (DEA), which the focus of the main study and the parametric stochastic frontier analysis (SFA), which we will look into very briefly. Literature reviews on banks efficiency studies on both methods are fairly abundant by now. For example Weill (2004), Ferrier and Lovell (1990), Sheldon (1994), Resti (1997), Bauer et al. (1998), Casu and Girardone (2002), Weill (2004) and Beccalli et al. (2006) are all Studies that compare parametric and non-parametric techniques using an identical data set.

During the late sixties stochastic frontier analysis (SFA) method experienced large popularity due to the influential work of Aigner and Chu (1968) that developed the econometric regression approaches and Aigner et al. (1977) and Meeusen and van den Broeck (1977), among others. The model is denoted in logs as ln(yj) = lnxj_+vj−uj , where xj denotes an input vector for firm j, vj depicts random error added to the non-negative inefficiency term, uj . This is stochastic because the upper limit is determined by the stochastic variable exp(xj_ + vj).

In Ferrier and Lovell (1990), they study the cost structure of 575 US banks for the year 1984 using both the SFA and DEA methods. In their result they find higher efficiency scores with DEA compared to SFA, namely 80% and 74%, respectively; concluding that DEA is sufficiently flexible to envelop the data more closely than the translog cost frontier.

However, efficiency scores are not significantly correlated thus indicating that other factors not controlled for may drive the obtained wedge between the two measures. European evidence is provided by

Sheldon (1994) study the cost efficiency of Swiss banks with SFA and DEA in the period from 1987 to 1991. In his results, DEA shows that the average degree of cost efficiency is about 56%, compared to SFA 3.9% mean efficiency.

Using two-stage DEA method, Bhattacharya et al. (1997), study the impact of Liberalization on efficiency of the Indian banking industry. During the first stage, a technical efficiency score was calculated, and in the second stage a stochastic frontier analysis was used to attribute variation in efficiency scores to three sources: temporal, ownership and noise component.

Also using a two stage DEA method, Seiford and Zhu (1999) study the performance of the top 55 US banks and their results showed that relatively large banks performed better on profitability, while the smaller banks performs better with respectively to marketability.

Likewise, Amel et al (2004), using both the SFA and DEA methods, he reports insignificant rank-order correlation of 1%, that showed no relationship between the two efficiency methods scores.

And Resti (1997), studying the cost efficiency of 270 Italian banks over the period 1988-1992. By comparing the parametric and non parametric efficiency, find out that econometric and linear programming results (SFA and DEA is statistically significant at the 1% level and ranges from 44% to 58%) do not vary significantly. and Furthermore, contrary to Ferrier and Lovell (1990) and Sheldon (1994), he reports higher efficiency scores between 81% and 92% for SFA as opposed to DEA scores between 60% and 78%.

Berger and Humphrey (1997), study of efficiency by using the nonparametric DEA and parametric SFA methods. In their result they found that the mean efficiency of nonparametric was 0.72 compared to the mean efficiency of parametric method which is 0.84. in Addition to their result, they noted that the rankings of these banks often found to be relatively different: foe example; in one study the rank correlation coefficients between rankings from parametric and nonparametric models were found to be 0.02 and in another study it was between 0.44 to 0.59.

In a more recent study, Casu and Girardone (2002), using SFA and DEA during the 1990s to measure the cost, profit efficiency of Italian financial banks. Their result shows that there are reasonably similar in Efficiency measures from stochastic and deterministic frontiers.

Also Weill (2004) using SFA and and DEA to measure the cost efficiency of 688 banks from five European countries: France, Italy, Germany, Spain, and Switzerland during 1992 to 1998. He finds that Efficiency scores do not vary significantly across these methods and there is no positive relationship between any parametric method and DEA.

And Beccalli et al. (2006) using SFA and DEA to measure cost efficiency of Stock-market listed European banks in 1999 and 2000. Finds that DEA efficiency scores are more dispersed compared to SFA and Furthermore, SFA scores of 85% are slightly higher than DEA scores 83%

To draw these arguments to a close and as per Bauer et al. (1998) conclusion and looking at the above debate from various economists study, there is no single correct approach to identify with an efficient frontier, although both methods SFA and DEA look to respond to varying degrees of individuality of the data.

Fourthly, we will take a looks at data envelopment analysis (DEA) in a single county ad also in more than one country

Using DEA Method, Yildirim (2002), Study the efficiency of Turkish commercial banks between 1988 and 1999. His results suggested that during these sample periods; that both pure technical and scale efficiency measures showed a great variation and the Turkish commercial banks did not achieve sustained efficiency gains.

Favero and Papi (1995); by using the non-parametric (DEA) method to study the cross section of 174 banks in 1991, they measure the technical and the scale efficiencies of the Italian banking industry. In their empirical findings, the north-Italian banks were more efficient than south-Italian banks; and their efficiency measured was best explained by the bank Size and to a lesser extent by location.

By using DEA to measure the efficiency of one largest commercial banks in the eastern province of Saudi Arabia, sample of 15 bank branches using a one year data, Al-Faraj et al. (1993) found out that these banks branches were efficient based on eight inputs and seven outputs identified.

Also, Al-Faraj et al (2006) using DEA to study the efficiency of the Saudi commercial banking industry in the 2002 by comparing the Saudi commercial banks with the world mean efficiency scores. Their study for the Saudi commercial banks efficiency score compares very well with the world mean efficiency scores. They further recommended that Saudi banks should continue to adapt to new technologies and providing more services in order to sustain competitive advantages.

Nonparametric data envelopment analysis (DEA) in More than one country

Casu and Molyneux (2003) used DEA to study efficiency of European banking systems and their sample geographical coverage in that study included France, Germany, Italy, Spain and the United Kingdom from the period 1993 and 1997. The aim of the study was to find out if the productivity efficiency in that area has improved and meet a common European frontier. But in their results, it was pointed out that these country banking systems were in a low average efficiency levels. Nevertheless, slight improvement was detected in the scores over the period of analysis for most of the banking systems; with the exception of Italy.

Conversely, in Casu, Girardone and Molyneux (2004) study of efficiency using DEA in European banking systems, geographical coverage of France, Germany, Italy, Spain and United Kingdom from the period 1994 – 2000, they found out that Italian banks has increase it efficiency level by 8.9%, and the reason for this improvement in efficiency was due to the cost reduction that the banks managed to attain. Further attained respected was achieved by the other country banks; Spanish banks increased by 9.5% , Germany banks increased by 1.8%, French banks also increases 0.6% and the English banks increased by 0.1% respectively.

Using a cost function method Allen and Rai (1996) study surveyed was fifteen countries financial institution: Australia, Austria, Canada, Switzerland, Germany, Denmark, Spain, Finland, France, Italy, United Kingdom, Sweden, Belgium, Japan and US. In their result; large banks showed the largest measure of input inefficiency and had anti-economies of scale; Italian banks, along with French, UK and US ones were found less efficient from Japanese, Austrian, German, Danish, Swedish and Canadians ones while the small banks had significantly lower inefficiency measures.

In Altunbas and Molyneux (1996), study of efficiency in France, Germany, Italy and Spain banking system, for economies of scale and scope; their result showed that there are differences among the four banking system regarding economies of scale. However, the Italian banks were indicated as significantly efficiency as they succeeded in lowering costs.

Pastor, Perez and Quesada (1997) study of efficiency using the non-parametric DEA method together with the Malmquist index, they compared the efficiency of United States, Spain, Germany, Italy, Austria, United Kingdom, France and Belgium banking system for the year 1992. Their study used the value added approach and in their results; the France banking system had the highest efficiency level followed by Spain, while UK banking system was presented to be lowest level of efficiency.

In Bikker (2001) study of the banks efficiency using a sample of European banks in various countries, along with Italy bank, during the period 1989-1997. In his result is was showed that the Spanish banks, followed by the French and the Italian banks; were the most inefficient banks; while the most efficiency banks were the one in Luxemburg, in Belgium and in Switzerland.

Also studying the efficiency of European Banking industry by Schure, Wagenvoort and O’Brien (2004) from the period 1993-1997; they found out that larger commercial banks were more efficiency on average than smaller banks. However, the Italian and the Spanish banks were found to be the in-efficient.

In the literature review, it can be seem that various studies have attempted to measure the efficiency of banks in the West and other parts of the world, although only few studies has focused on measuring the efficiency in the UK Commercial banks. Hence the aim of the dissertation will be to fill this research gap by empirically measuring the efficiency in the UK Commercial banks using the nonparametric DEA method.